ON BOUNDS OF RADIO NUMBER OF CERTAIN PRODUCT GRAPHS

D. O. AJAYI, T. C. ADEFOKUN

Abstract

Given a graph $G$, whose vertex set is $V(G)$, the radio labelling of $G$ is a variation of vertex labelling of $G$ which satisfy the condition that given any $v_1,v_2 \in V(G)$, and some positive integer function $f(v)$ on $V(G)$, then $|f(v_1)-f(v_2)| \geq \textmd{diam}(G)+1-d(v_1,v_2)$. Radio labelling guarantees a better reduction in interference in signal-dependent networks since no two vertex have the same label. The radio number $rn(G)$ of $G$ is the smallest possible value of $f(v)$ such that for any other $v_k \in V(G)$, $f(v_k) < f(v)$. In this work, we consider a Cartesian product graph obtained from a star and a path and determined upper and lower bounds of the radio number for the family of these graphs.